The uploaded document contains a series of mathematical problems mostly centered around arithmetic and geometric sequences. Let's address each question one by one:

1. Question: The first few terms of a sequence are given as 4.9, 14.9, 24.9, ... The task is to identify the common difference and the formula for the nth term of the arithmetic sequence.

   • Solution: The common difference (d) can be found by subtracting the first term from the second term: $d = 14.9 - 4.9 = 10$. The nth term of the arithmetic sequence can be expressed as $a_n = a_1 + (n-1)d$, where $a_1$ is the first term. Thus, $a_n = 4.9 + (n-1) \times 10$.

2. Question: Determine the nth term of the sequence where the second term is 17.1, the fourth term is 17.3, and the terms form an arithmetic sequence.

   • Solution: The common difference is calculated as $d = (17.3 - 17.1) / 2 = 0.1$. The nth term formula becomes $a_n = 17 + 0.1n$, setting the first term $a_1 = 17$ (because $a_2 = 17.1$).

3. Question: If the 7th term of a sequence is 20, and the 15th term is 3, find the nth term.

   • Solution: Using the arithmetic sequence formula $a_n = a_1 + (n-1)d$, with the given $a_7 = 20$ and $a_{15} = 3$, we find $d = (3 - 20) / (15 - 7) = -17/8 = -2.125$. The first term $a_1$ can be determined by substituting back into the formula for any term.

4. Question: The sequence describes the number of chairs in rows, increasing by three each row: 14 chairs, 17 chairs, etc. The task is to find the total number of chairs in the 20th row.

   • Solution: This forms an arithmetic sequence where $a_1 = 14$, $d = 3$. For the 20th row, $a_{20} = 14 + 19 \times 3 = 71$.

5. Question: Calculate the sum of the first ten terms of the sequence $-5, -8, -11, -14, \ldots$.

   • Solution: This is an arithmetic sequence where $a_1 = -5$, $d = -3$. The sum of the first 10 terms $S_{10}$ can be calculated using the sum formula $S_n = \frac{n}{2} \times (2a_1 + (n-1)d)$.

6. Question: Given $a_6 = 17$ and $a_{10} = 33$ of an arithmetic sequence, find $S_{20}$.

   • Solution: First find $d$ and $a_1$ using the given terms, then use $S_n = \frac{n}{2} \times (2a_1 + (n-1)d)$.

7. Question: For a sequence starting with 168 and decreasing, the task is to calculate $a_{12}$.

   • Solution: Given $S_{12} = 168$, use the sum formula in reverse to find $a_1$ and $d$, and subsequently find $a_{12}$.

These are the solutions for the first seven questions. Would you like to proceed with the remaining questions or need detailed explanations for any specific question among these?